CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
A collimated beam of ideal gas molecules, each of mass m and identical speed v, strikes a large stationary plane surface. The beam makes an angle θ with the surface normal (so θ=0∘ corresponds to head-on incidence). The number density of molecules in the beam is nbeam. Assume that all molecules are reflected elastically so that their speed remains v and the angle of reflection equals the angle of incidence.
(a) For a single molecule in the beam, determine the change in the component of its linear momentum that is perpendicular to the surface during one collision.
(b) Express the collision rate (number of molecules striking a unit area of the surface per unit time) in terms of nbeam, v, and θ.
(c) Combine your results from parts (a) and (b) to derive an expression for the pressure exerted on the surface by the beam as a function of nbeam, m, v, and θ.
(d) Evaluate your expression at θ=45∘ and at θ=0∘. Explain physically why the pressure decreases when the beam is more oblique.